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Full Idea
There is no logical reason against infinite collections, and we are therefore justified, in logic, in investigating the hypothesis that there are such collections.
Gist of Idea
We may assume that there are infinite collections, as there is no logical reason against them
Source
Bertrand Russell (Introduction to Mathematical Philosophy [1919], VIII)
Book Ref
Russell,Bertrand: 'Introduction to Mathematical Philosophy' [George Allen and Unwin 1975], p.77
Related Idea
Idea 15931 The iterative conception needs the Axiom of Infinity, to show how far we can iterate [Lavine]
| 22288 | We have the idea of self, and an idea of that idea, and so on, so infinite ideas are available [Dedekind, by Potter] |
| 18104 | Frege, unlike Russell, has infinite individuals because numbers are individuals [Frege, by Bostock] |
| 14440 | We may assume that there are infinite collections, as there is no logical reason against them [Russell] |
| 14447 | Infinity says 'for any inductive cardinal, there is a class having that many terms' [Russell] |
| 13430 | Infinity: there is an infinity of distinguishable individuals [Ramsey] |
| 10051 | The axiom of infinity is not a truth of logic, and its adoption is an abandonment of logicism [Kneale,W and M] |
| 13037 | Infinity: ∃x (0 ∈ x ∧ ∀y ∈ x (S(y) ∈ x) [Kunen] |
| 17800 | The misnamed Axiom of Infinity says the natural numbers are finite in size [Mayberry] |
| 13021 | The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy] |
| 13022 | Infinite sets are essential for giving an account of the real numbers [Maddy] |
| 18191 | Axiom of Infinity: completed infinite collections can be treated mathematically [Maddy] |
| 10878 | Infinity: There exists a set of the empty set and the successor of each element [Clegg] |
| 13044 | Infinity: There is at least one limit level [Potter] |